Option C:
It is [tex]\frac{1}{3}[/tex] throughout the line.
Solution:
Point on the larger shaded triangle are (0, 0) and (–6, –2).
Point on the smaller shaded triangle are (–6, –2) and (–9, –3).
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Slope of the larger triangle:
Here, [tex]x_{1}=0, y_{1}=0, x_{2}=-6, y_{2}=-2[/tex]
[tex]$m=\frac{-2-0}{-6-0}[/tex]
[tex]$m=\frac{-2}{-6}[/tex]
[tex]$m=\frac{1}{3}[/tex]
Slope of the smaller triangle:
Here, [tex]x_{1}=-6, y_{1}=-2, x_{2}=-9, y_{2}=-3[/tex]
[tex]$m=\frac{-3-(-2)}{-9-(-6)}[/tex]
[tex]$m=\frac{-3+2}{-9+6}[/tex]
[tex]$m=\frac{-1}{-3}[/tex]
[tex]$m=\frac{1}{3}[/tex]
Both slopes are equal.
It is [tex]\frac{1}{3}[/tex] throughout the line.
Hence option B is the correct answer.
